"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Wednesday, January 28, 2015

Why Cramming Does Not Work

Back in high school, we had regular weekly quizzes on current events. The quizzes were based on the contents of a bulletin that we were required to buy and read. Since the questions required a simple retrieval of information, I often read and memorized as much as I could within an hour before the quiz. After all, the quiz was only measuring a sciolistic or superficial knowledge of what was in the news. Whether I would retain the information hours after I took the quiz did not really matter.

A quiz that requires only frivolous pieces of information is where cramming works best. It does not work in mathematics or in the sciences, especially when problem solving is expected. To solve problems requires first and foremost a correct choice of strategy. A final exam in chemistry, for instance, can cover so many chapters and a large part of the exam relies on a student correctly recognizing what topic is being covered by the question and choosing the appropriate approach. This is likewise true in mathematics. Cramming only involves memorizing large amounts of information in a short period of time. Due to lack of practice and time to digest, it is not possible for a student who only crams to relate and identify different strategies and problems.

Courses in schools are usually structured into various lessons. Lessons are drawn based on topics. It is therefore common to see lessons that focus on a topic or two. In third grade, students may spend some time, for example, four weeks, learning multiplication. Then the next four weeks may be devoted to learning fractions. And another four weeks may be focused on decimal places. With cognitive load in mind, it is important to lecture on one topic at a time. With regard to activities and homework, it is not necessary to limit an assignment within the topic currently discussed or taught in class. It is possible to add questions from topics previously covered. Doing this allows for students to see problems of various kinds. Questions are not necessarily on the topic at hand. It is only through this mixing that a student receives an opportunity to practice identifying problems, making choices, and drawing appropriate strategies. Rearranging problems in students' activities or homework so that the questions do not belong to one topic is called interleaved practice.

Several studies have shown that interleaved practice is superior to blocked practice (activities or homework that focus only on one topic or one style of problem). For instance, a recent study published in the Journal of Educational Psychology, shows that interleaved practice leads to better results even when a review session is provided. This study takes place in a middle school in Florida. The lessons covered include graphing and calculating slopes. One group of students receives practice problems that are solely on the topics covered while another group has to work on problems from previous topics such as fractions, proportions, percentages, statistics and probability in addition to the problems on graphing and slopes. Both groups are provided a review session a day (or thirty days) before the unannounced test on graphs and slopes.

And the results are summarized in the graph below:

Above copied from Rohrer et al.
After a month has passed after the review session, students who are taught in an interleaved fashion demonstrate far better retention of what is learned during the lessons on slopes and graphs.

During my high school years, I would have probably remembered more and understood better what was going on if those quizzes were based not only on the weekly bulletin at hand but also on previous ones. Seeing a concrete example of an interleaved activity is perhaps useful at this point so I am sharing here a homework that my son has just received from his teacher. My son is just beginning to study division at the moment. His class has finished addition and subtraction with numbers containing multiple digits, fractions, making estimates, decimal places, and number lines. The homework below obviously does not contain only division questions:

Seeing the above set makes it quite obvious that a student working on this homework needs to identify the problem first. From there, a student then chooses the appropriate strategy. The questions do not fit under one topic or category. This practice, based on controlled studies such as the one published by Rohrer et al., leads to better performance and a longer retention of knowledge and skills.

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Tuesday, January 27, 2015

"You're a Teacher, What a Waste!"

"...You graduated from a very good university, and you’re in a public school?” “What a waste!... ...Then I realized, it’s not about my decision to be a public school teacher. It’s about what people think of our public schools. If our public schools were well run, people won’t be telling me those things." These are the words of Sabrina Ongkiko, an alumnus of Ateneo de Manila University who decided to teach in a school where a teacher's socks and shoes can be easily drenched when it rains because of leaky roofs. Sabrina correctly sums up one of the gravest ills of public basic education. Unfortunately, we are always quick to point our blaming fingers on teachers when the missteps are really from the top, education policy makers and the government.

There are isolated bright spots like the story of Sabrina. Unfortunately, the image of teaching in a public school has been so tarnished that these spots can be easily overwhelmed by the darkness that currently engulfs Philippine schools. Seeing what is happening in New York State makes one envious. A paper recently published in the journal Educational Researcher shows that individuals entering the teaching profession are increasingly coming from the top-performing students. 
Above copied from Educational Researcher 
The turnaround is truly remarkable and it starts at the turn of the century. And from 2006-2010, the proportion of teachers coming from the upper third in terms of SAT scores is now about to reach 50 percent. What is more remarkable however is the fact that schools serving a larger number of students from poor families are the chosen destinations of these promising new teachers as seen in the following figure:

Above copied from Educational Researcher 
Of course, there still remains plenty of room for improvement. As demonstrated in the above figure, schools with the highest poverty are still behind other schools in terms of SAT scores of the teachers. The richest schools still have the highest combined SAT score among the teachers. But the trend is nonetheless encouraging. Perhaps, the attitude is indeed turning around and the image of the teaching profession is slowly improving. 

Someday, this may likewise happen in the Philippine schools. But that day will only arrive when those who are causing great damage to basic education are no longer drawing policies and curriculum.

Monday, January 26, 2015

How We Teach Arithmetic

One way a five-year old could be taught addition is by using flash cards. It is true that for some, this may sound as pure memorization. What is obviously needed is not only to remember but also to acquire the ability to relate and manipulate which then leads to a deeper understanding of arithmetic. A child of course can develop this understanding if the child has first memorized addition facts. This is not different from knowing sight words which immensely helps young minds to read. Having the facts frees up some space in a child's working memory which a child can then use to find patterns and relationships, and begin to appreciate the world of mathematics. Since a kindergarten or first grade teacher already knows what lies ahead, memorization drills can be tailored such that students can likewise anticipate what is coming. Instead of a randomly or iteratively (which may aid in memory) arranged set of flash cards, addition facts can be presented with the objective of preparing students for higher math. Such approach is nicely illustrated in a poster presented by McNeil and coworkers at the University of Notre Dame. The following is a figure taken from the poster:

Above copied from McNeil et al.
Flash cards or activities can be easily modified to achieve so much more than just practicing addition facts. In another poster by Mcneil and coworkers, the following pair of activities nicely highlights what can be achieved by introducing minute changes on elementary flash cards. The following activity, for example, aims only for the minimum (helping a child learn to count and add):

A child learns to count dots and the numbers associated with each count. A child also learns to combine the dots from each box and therefore performs the addition operation. The following, on the other hand, with just simple modifications, can achieve so much more:

Above copied from McNeil et al.

The activity demands exactly the same thing from a student: Count the dots and provide the number that is associated with a particular count. However, by simply rearranging what is known, the child is now being introduced to subtraction. In addition, it may look trivial but the mere replacement of the "=" sign by the phrase "is the same amount as", is actually a big deal in the mind of a young child.

The modifications are small yet the gains appear substantial in the assessment results. For instance, by simply grouping addition facts by equivalence, the following is obtained:

Above copied from McNeil et al.
By rearranging addition facts so that the children sometimes solve for numbers on either side of the equation also yields significant improvements:

Above copied from McNeil et al.

It does make a difference when teachers tailor their lessons and students' activities with specific objectives. These still look like drills but these help students gain a better understanding of the lesson. And it seems to require not much effort. To read more on this topic, McNeil and coworkers have published their work in the Journal of Educational Psychology:

The above results are indeed convincing. What is troubling, however, is the fact that the mean age of the children participating in this study is over 8 years old (second grade). To see that the children are able to get less than 50 percent correct on the assessments is truly distressing. Children in this study are from a disadvantaged background, showing that a lot of work still needs to be done. Interventions shown above yet simple and cheap are making a difference.

Saturday, January 24, 2015

Attention and Working Memory

Last night, my two children and I had a mental activity. First, I recited four digits and they had to recite them in the reversed order. Both were able to do it. Then we started working on five digits. They still could do it, and we even reached seven. This is an example of measuring an individual's number storage capacity. The span of digits an individual can recall and recite backward quantifies working memory. Working memory is like a mental scratch pad on which information is both stored and manipulated.

Above copied from Landmark College

The following data correspond to eight-year old children. Seeing this table explains why I am a bit surprised that my son could do seven digits in reverse order.

WISC-IV® DIGIT SPAN DATA FROM TABLE B.7, p. 267 Wechsler Intelligence Scale for Children -- David Wechsler © 2003 The Psychological Corporation, San Antonio TX

Working memory is one characteristic that is found to correlate strongly with academic performance in the early years. Another characteristic is the ability to focus or concentrate. A lack of attention or inattention has been strongly associated with poor performance in both mathematics and reading comprehension.

Above copied from Landmark College

Seeing that both working memory and attention appear to be crucial in the early years, there are various interventions out there advertised to help children develop both working memory and attention. An example is shown below from LearningRx:
Above copied from the NewYork Times
Whether these interventions are effective or not still remains to be adequately answered by well-controlled or well-designed experimentation. What is clear is that both working memory and attention strongly correlate with academic achievement in the early elementary years as illustrated by a recent study published in the Journal of Educational Psychology:

Above copied from the Journal of Educational Psychology
What is noteworthy in the above study is that the relationship apparently fades in the later years. One must keep in mind that the above study like most research in education is a mere observation of a correlation and not necessarily causation. Furthermore, there are specific relationships found in the study that appear quite puzzling. One example is the observation that a child's ability to retell a story predicts initial math performance but not reading comprehension. Being able to recall details of a story, on the other hand, does relate to better performance in reading comprehension, but does not correlate with growth in math competency. On the other hand, the backward digit span task (the activity described at the beginning of this post) correlates very well with performance in both reading and math.

What is truly inside the relationship between working memory, attention, and academic achievement is still unknown. If I would hazard a guess, the relationship between academic tasks and cognitive abilities might even be bidirectional. Both attention and working memory grow with a child. Clearly, these skills may be caught or learned through the elementary years. It is possible that a child does improve his or her working memory by working on math activities inside school. It is possible that reading activities enhance a child's cognitive skills. Oftentimes, too much emphasis is placed on what a child has. After all, schools are supposed to help a child grow and develop.  Thus, what is measured in the above study may just be the outcomes from spending some useful time in schools and that is why there is a correlation.

Going back to my grade school years, I did have teachers who had always demanded my attention. I had teachers who inspired me to work harder. Whether it is the inspiration or the attention that actually led to my satisfactory performance is not clear since my teachers also taught me how to add, subtract, multiply, divide, read and write. These were all in one package....

Thursday, January 22, 2015

How Well Do Our Teachers Know Arithmetic?

Arithmetic knowledge is as essential as literacy. Arithmetic knowledge must go beyond whole numbers since fractions or percentages appear in almost every occupation, even in fields outside of STEM (Science, Technology, Engineering and Mathematics). As a typical example, leaving a correct tip in a restaurant requires fraction arithmetic. Arithmetic knowledge involves both operation and concepts. It is important not just to know how to add, subtract, multiply and divide but also to understand what these operations really entail. After all, calculators can do all of these operations. A conceptual understanding of arithmetic operations cannot be obtained from a calculator. Such understanding is crucial to both science and engineering. It is equally advantageous for a society as a whole if individuals have a sense of what numbers and operations really mean. Arithmetic errors can be often spotted and good estimates can be made without actually performing the calculations.

A more recent example of how fractions may creep into our daily lives is the question of whether the Patriots intentionally deflated their balls or not. A science teacher posted the following on Reddit:

[–]Patriotsniknight_ml 35 points  
Science teacher here. Given the conditions of the game, a ball which meets specifications in the locker room could easily lose enough pressure to be considered under-inflated. Some math:
  • Guy-Lussac's Law describes the relationship between the pressure of a confined ideal gas and its temperature. For the sake of argument, we will assume that the football is a rigid enough container (unless a ball is massively deflated, it's volume won't change). The relationship is (P1/T1) = (P2/T2), where P is the pressure and T is the temperature in Kelvins.
  • The balls are inflated to between 12.5 and 13.5 psi at a temperature of 70 degrees Farenheit (294.1 K). Let's assume an average ball has a gauge pressure of 13 psi. This makes the absolute pressure of the ball 27.7 psi (gauge + atmosphere). Since these are initial values, we will call them P1 and T1.
  • The game time temperature was 49 degrees F (282 K). We are attempting to solve for the new pressure at this temperature, P2. We plug everything into the equation and get (27.7/294.1) = (P2/282). At the game time temperature, the balls would have an absolute pressure of 26.6 psi and a gauge pressure of 11.9, below league specifications.
(Note: I have made corrections to the above post (in blue) since the author originally made an error in converting 49 degrees Fahrenheit to Kelvin)

Wednesday, January 21, 2015

Teamwork Versus Excellence: Is This Another False Dichotomy?

On one hand, we read that working together leads to better results. Take for example, a post from the blog of the United States Department of Education where a quote from a public school teacher in Springdale, Arkansas is highlighted: "I used to think about just my classroom. Now, I care about the collective whole of fourth grade." Teamwork, according to the principal in this school, has led to substantial gains in student learning simply by having teachers work as a team and believing that each student can succeed at very high levels.

Watching the video above leaves me with the following phrases:

"We have teachers that believe in each and every student and their potential."

"We make all decisions at our school based on what the data tell us."

"We are able to separate our students into who is doing really well, who is at grade level, and who is not, but not what it means by the child, but what it means by our teaching."

"There is no shame in reaching out for help."

"We really focus on growth."

And the results are quite dramatic:

The above does appear quite convincing. Teamwork leads to better schools. Until one comes across another blog. This one is from TeachThought. The following is an excerpt:
When we ask for great teachers, then, it’s not clear if we all mean the same thing when we use the term. What’s a great teacher? If nothing else, by definition a great teacher is going to be exceptional. Different. If everyone is extraordinary, no one’s extraordinary. 
A great teacher navigates the boundaries of policy, content, and the sensitivity of people to get the clearest view of students. The most important gift a teacher has is the ability to see children for who they are, who they can be, and the relationship between the two. They have the unique ability to see students and content and thought and ideas and then nothing else—a blindness to irrelevance that lets the rest of the world melt away. They see your literacy plan, and your assessment policy, and your hashtag, and your app—but they see it within a macro context that it doesn’t matter—and can’t survive–without. 
This means that they might not “buy-in” to the new district initiatives. They may question the $500,000 iPad “rollout.” They might resist the testing if all of the data is just going to sit there without substantively altering future curriculum and instruction. They may not be the stars of the PLC. 
And unless they have enough charisma to pull it all off, it’s all going to cost them their “team-player” reputation.
It is a false dichotomy. Even in sports, a great basketball player is likewise a great team player. Problems often creep into the picture for other reasons. Teamwork only provides an environment where strengths can be shared and weaknesses addressed. The phrases mentioned above are all sound and good but these all lose luster in the face of pretense or incompetence. The fact that a great teacher is one who is able "to see students and content and thought and ideas and then nothing else" means that one simply has to keep in mind that the goal is not to be a dream team, but to teach children.

Echoing Alfie Kohn's sentiment:
A skunk cabbage by any other name would smell just as putrid. But in education, as in other domains, we’re often seduced by appealing names when we should be demanding to know exactly what lies behind them. Most of us, for example, favor a sense of community, prefer that a job be done by professionals, and want to promote learning. So should we sign on to the work being done in the name of “Professional Learning Communities”? Not if it turns out that PLCs have less to do with helping children to think deeply about questions that matter than with boosting standardized test scores.

Monday, January 19, 2015

"Practice Makes Perfect"

My family did not have a stable source of income while I was growing up. Wearing the same pair of pants throughout the entire school week was not a matter of choice. I only had one pair of pants. I certainly would meet the description of a disadvantaged student. In addition, I was obviously an English language learner. Factors outside school were clearly not in my favor. I was aware that I was different and disadvantaged, but like any child, I desired to be like my classmates. Being wealthier, I knew, was clearly out of my reach then, but having the same aspiration and dreams, on the other hand, was within my grasp.

Peer pressure is real. What happens inside one's home may seem very influential on a child but upon closer examination, chats that occur inside a playground oftentimes weigh more. A child after all spends most of his or her waking hours not at home but at school. What a child likes to watch on television is shaped by what his or her friends watch. Books that catch the interest of a child's mind are frequently those that contain stories and characters shared with peers. How a child performs in school is deeply influenced by what the child sees in others. When those examples are the correct ones, a child can easily overcome the disadvantages of being poor and challenged.

My personal story is purely an anecdote. But there are others that relate the same story. One example is the PracticeMakesPerfect program based in New York City:

Practice Makes Perfect addresses inequities in socioeconomically disadvantaged neighborhoods over the summer. Research has found that two-thirds of the ninth-grade achievement gap between lower and higher income youth can be explained by unequal access to summer learning opportunities. Students from low-income areas lose between 2.5 to 3.5 months of academic learning each summer, while their affluent peers are making academic gains. 
Our Model

Practice Makes Perfect is a comprehensive summer education program with a proven “near-peer” model to support students from kindergarten through college matriculation. Our programs pair skills development for younger students with leadership development, career training and college prep for older students. Through a unique multi-relational approach, Practice Makes Perfect strategically matches academically struggling elementary and middle school students with older, higher achieving mentor peers from the same inner-city neighborhoods. Trained college interns and certified teachers supervise the “near-peer” relationship for a five-week, full-day academic experience.

And the results of this program are quite promising:

It is therefore clear why inclusive education is a must...

Sunday, January 18, 2015

"Reality Is Superior to Ideas"

Korea.net / Korean Culture and Information Service (Jeon Han) [CC BY-SA 2.0], via Wikimedia Commons

Full text of the message of Pope Francis to the youth

University of Santo Tomas

January 18, 2015

When I speak spontaneously, I do it in Spanish because I don’t know English language. May I do it? Thank you very much. Here’s Father Mark, a good translator.

[As delivered by translator. Text in bold letters are spoken by the Pope himself.]

The sad news today: Yesterday, as mass was about to start, a piece of the scaffolding fell. And upon falling, it hit a young woman who was working in the area, and she died. Her name is Crystal. She worked for the organization and preparation for that very mass. She was 27 years old, young like yourselves. She worked for those Catholic relief services, a volunteer worker.

I would like all of you, young like her, to pray for a moment in silence with me and then we pray to Mama, our lady, in heaven. [silence] “Hail Mary, full of grace, the Lord is with thee. Blessed art thou amongst women and blessed is the fruit of thy womb Jesus. Holy Mary, mother of God, pray for us sinners, now and at the hour of our death, Amen.”

Let us also pray for her parents. She was the only daughter. Her mom is coming from Hong Kong and father come to Manila to wait. “Our Father, who art in heaven, hallowed be thy name; thy kingdom come; thy will be done on earth as it is in heaven. Give us this day our daily bread and forgive us our trespasses, as we forgive those who trespass against us, and lead us not into temptation but deliver us from evil.”

This is special for me to greet you this morning. I greet each of you from the heart and I thank all those who made this meeting possible. During my visit to the Philippines, I want in a particular way to meet young people; to listen to you and to talk with you. I want to express the love and the hopes of the Church for you, and I want to encourage you as Christian citizens of this country to offer yourselves passionately and honestly to the great work of renewing your society and helping to build a better world. In a special way, I thank the young people who have helped the worlds that they’re going to meet.

To Jun and Leandro and to Rikki, thank you very much. And only a very small representation of females among you, too little. [laughter] Women have much to tell us in today’s society. [laughter, applause] Sometimes we’re too ‘machistas’ and we don’t allow room for the woman. But women are capable of seeing things from a different angle to us, from a different eye. Women are able to pose questions that we, men, are not able to understand. Look out for this fact today: She, Glyzelle, is the only one who has put a question for which there is no answer. And she wasn’t able to express it in words but, rather, in tears. So, when the next Pope comes, please more girls, women, among the number. [cheers, applause]

I thank you, Jun, that you have expressed yourself so bravely. The nucleus of your question, as I said, also almost doesn’t have a reply. Only when we, too, can cry about the things we just said are we able to come close to replying to that question. Why do children suffer so much? Why do children suffer? When the heart is able to ask yourself and cry, then we can understand something. There is a worldly compassion, which is useless. You spoke something of this. It’s a compassion, which, moreover, leads us to put our hand into the pocket and give something to someone, to the poor. If Christ had had that kind of compassion, He would have walked by, just two or three people, giving them something and moved on. But it’s only when Christ cried and was capable to cry that He understood our lives, what’s going on in our lives.

Dear girls, boys, young people, today’s world has a great lack of capacity of knowing how to cry. [-unclear-] Those that are left to one side are crying. Those who are discarded, those are crying, but we don’t understand much about these people without these necessities. Certain realities in life we only see through eyes that are cleansed through our tears. I invite each one of you here to ask yourself: Have I learned how to weep, how to cry? Have I learned how to weep for somebody who’s left to one side? Have I learned to weep for someone who has a drug problem? Have I learned to weep for someone who suffered abuse? Unfortunately, those that cry [was] because they want something else.

This is the first thing I’d like to say: Let us learn how to weep as she has shown us today. Let us not forget this lesson. The great question of why so many children suffer? She did this crying and the response that we can make today is – let us learn, really learn how to weep, how to cry. Jesus in the gospel, He cried. He cried for his dead friend. He cried in his heart, for the family that had list its child. He cried when he saw the poor widow having to bury her son. He was moved to tears, to compassion when he saw the multitude of crowds without a pastor.

If you don’t learn how to cry, you can’t be good Christians. This is a challenge. Jun and Glyzelle have posed this challenge to us today, and when they posed this question to us—why children suffer, why this and that tragedy occurs in life—our response must either be silence or a word that is borne of our tears. Be courageous; please don’t be frightened of crying.

Then came Leandro Santos II and his question. He also posed the questions, the world of information. Today, with so many means of communications, we are overloaded with information. Is that bad? Not necessarily. It is good and it can help. But there is a real danger of living in a way of accumulating information. We have so much information, but maybe we don’t know what to do with that information. We’re on the risk of becoming museums of young people that have everything but without knowing what to do with them. We don’t need youth museums, but we do need holy young people.

You might ask me: ‘Father, how do we become saints?’ This is another challenge. It’s the challenge of love. Which is the most important subject that you have to learn in university? What is the most important subject you have to learn in life? To learn how to love and this is the challenge that life offers you: To learn how to love and not just accumulating information without knowing what to do with it. But through that love, that information bear fruit.

After this, the gospel offers us a serene path and way forward. Use the three languages: of the mind, of the heart, and of your hands. And the three, to use them in harmony: What you think, you must feel and put into effect. Your information comes down to your heart and you realize it in real works. And this, harmoniously. Think what you feel and what you do. Feel what you think and feel what you do. You do what you think and what you feel—the three languages. Can you repeat this? To think, to feel, and to do. To think, to feel, and to do. To think, to feel, and to do. And all that, harmoniously.

Pope Francis, center, dances with Filipino children during his meeting with the youth at the University of Santo Tomas in Manila, Philippines Sunday, Jan. 18, 2015. Francis opened his meeting with the Filipino youth on a somber note, reporting to thousands gathered at the centuries-old university the sad news that a female church volunteer had died during his visit to central Tacloban city the previous day, and led prayers for the woman. At top left with a red sash is Filipino Cardinal Luis Antonio Tagle. (AP Photo/Aaron Favila)

Real love is about loving and letting yourselves be loved. Let yourselves to be loved. That is why it’s so difficult to come to perfect love of God because we can love him, but it is so important to let yourselves be loved by him. Real love is opening yourselves to the love that wants to come to you, which cause a surprise in us. If you only have information, then the element of surprise is gone. Love opens you to surprise and is a surprise because it presupposes dialogue between the two: of loving and being loved.

And we say that God is a God of surprises because He always loved us first and he awaits us with a surprise. God surprises us. Let us allow ourselves to be surprised by God. Let us not have the psychology of the computer: to think that we know it all. All the responses on the computer screen have no real surprise. The challenge of love: God reveals himself through surprises.

Let’s think of St. Matthew. He was a good financier and he let people down because he imposed taxes against his own citizens, the Jews, to give to the Romans. He was full of money and charged these taxes. But then Jesus goes by, He looks at him, and He says ‘follow me.’ He couldn’t believe it. If you have time, go and see the picture that Caravaggio painted about the story. Jesus calls him and those around him said ‘this one? He has betrayed. He’s no good and he holds money to himself.’ But the surprise of being love overcomes him.

It is this way. The day when Matthew left his home, said goodbye to his wife, he never thought he was going to come back without money, and worried and concerned about how to have such a big feast—to prepare that feast for Him who have loved him first, who surprised Matthew. It’s something very special, more important than the money that Matthew had. Allow yourselves to be surprised by God and don’t be frightened of surprises. They shake the ground from underneath your feet and they make us unsure, but they move us forward in the right direction.

Real life, real love leads you to spend yourselves in life, to leave your pockets open and empty. St. Francis died with empty hands, with empty pockets, but with a very full heart. So, no young museums, wise young people. To be wise, use the three languages: to think well, to feel well, and to do well. And to be wise, allow yourselves to be surprised by the love of God, and that’s a good life. Thank you.

He who came with a good plan was Rikki, to see how he can go in life. With all the activities, the multiple facets that accompany young people, thank you, Rikki. Thank you for what you do and your friends. I’d like to ask you, Rikki, a question: You and your friends are going to give help, but do you allow yourselves to receive? Rikki, answer in your heart.

In the gospel we just heard, the beautiful, which, for me, is the most important of all… He looked at the young man, Jesus Christ, and He loved him. When you see young group of friends, Rikki and his friends, who love so much because they do things that are really good. But the most important phrase that Jesus says, “You lack one thing.” Let us listen to these words in silence: “You lack only one thing. You lack only one thing… [Repeat] with us: “You lack only one thing. You lack only one thing.”

What is it that I lack? To all who Jesus loved so much, I ask you, do you allow others to give you from their riches to you that don’t have those riches? Sad to see that doctors of the law, in the time of Jesus, gave much to the people. They taught them but they never allowed the people to give them something. Jesus had to come to allow Himself to feel compassion, to be loved. How many young people among you are there like this? You know how to give and yet you haven’t yet learned how to receive. You lack only one thing: Become a beggar—to become a beggar. This is what you lack, to learn how to beg and to those to whom we give. This isn’t easy to understand: To learn how to beg. To learn how to receive with humility. To learn to be evangelized by the poor.

Those that we help, the poor, the infirm, orphans, they have so much to offer us. Have I learned how to beg also for that or do I feel self-sufficient and I’m only going to offer something and think that you have no need of anything? Do you know that you, too, are poor? Do you know your poverty and the need that you receive? Do you let yourselves be evangelized by those you serve, let them give to you?

And this is what helps you mature in your commitment to give to the others, to give to others: to learn how to offer up your hand from your very own poverty. There are some points that I prepared: to learn how to love and to learn how to be loved. It is a challenge, which is a challenge of integrity. This is not only because your country, more than many others, is likely to be seriously affected by climate change. It is a challenge to [have] concern for the environment. And finally, the challenge for the poor—to love the poor.

With the bishops, to ask in a very special way, for the poor. Do you think with the poor? Do you feel with the poor? Do you do something for the poor? Do you ask the poor that they might give you the wisdom that they have? This is what I wish to tell you all today. Sorry, I haven’t read what I prepared for you, but I’m consoled. Reality is superior to ideas. And the reality that you all have is superior to the paper in front of me. Thank you very much. Thank you.

Saturday, January 17, 2015

Calculations, Word Problems, and Algebra

Learning mathematics can be divided into several domains. Even in the early elementary years, with regard to numeracy, three separate domains can be defined. First, pupils need to understand magnitude as expressed in numbers. Second, pupils need to acquire skills in combining numbers, as in addition and subtraction. Third, pupils need to be able to process text and construct a number sentence to calculate the unknown. These three domains: understanding, calculation, and solving word problems are very important in early elementary mathematics.

At first glance, the domains may not seem entirely separate from each other. Having a "feel" for numbers, as observed even in higher education science classes, may help in both calculations as well as solving word problems. And understanding numbers by itself can manifest in different shades. For instance, the two questions shown below are quite different although both are simply assessing an understanding of numbers:

Above copied from IXL

Calculations and word problems, however, can be more easily distinguished from each other. Calculations are just straight addition and subtraction exercises, as demonstrated in the following example:

Above copied from Momonix

Word problems, on the other hand, require a student to translate text into a mathematical sentence:

Above copied from Mathplayground
The above text requires a student to recognize that the text is likewise asking the question "15 - 8 = ?". Here, at first glance, it could be suggested that solving word problems is simply a wider domain and calculation is simply one of the parts. After all, solving word problems do require calculations.

However, pedagogically, calculations and word problems can be vastly different. Interventions designed to hone a student's calculation skills may include practice in addition and subtraction, recognition of number families, associative operations, and other strategies. Addressing word problems, on the other hand, begins with language comprehension. A recent study published in the Journal of Educational Psychology shows that these two are indeed separate domains and are quite independent from each other.

As the above abstract states, "...calculation intervention improve calculation outcomes but not word-problem outcomes, word-problem intervention enhanced word-problem but not calculation outcomes...." This distinction makes it clear that pupils need to be taught and assessed in both domains.

The above study likewise points out that word-problem intervention may be providing a stronger route to algebra than calculations do, but I would exercise caution with this finding as algebra also involves these two separate domains:


Word Problem:

Nevertheless, I strongly agree with the author's major conclusion:

"...calculation and word-problem performance at second grade appear to represent distinct aspects of mathematical cognition and indicate the need to address calculation and word-problem performance deliberately and explicitly in research and practice."

Thursday, January 15, 2015

Reading in School, Reading for Fun

It is true that a love for reading needs to be nurtured not only in school but likewise inside children's homes. It is, however, much more practical to focus on how much a school contributes to a child's inclination to read since it is only within a school that educators could effectively draw and implement programs that enhances literacy. Schools cannot dictate what happens at home, but schools can design and support a curriculum that helps children develop a love for reading.

In 2014, YouGov conducted a study for Scholastic to explore what conditions correlate with children reading books for fun. Obviously, there are various factors at home that are expected to correlate with children's reading behavior. How much a parent reads to a child is a top factor. The recent study shows that more than half (54%) of children ages 0-5 are read aloud at home 5-7 days a week. At least seventy percent of homes surveyed read a book to a child before age one. And more than eighty percent of children across all ages (6-17 years) say they either like or love it when books are read aloud at home. These numbers are indeed encouraging when it comes to reading at home. The following shows that the attitude towards reading at home for young children is positive across most homes in the United States:

Above copied from Kids and Family Reading Report, 5th Ed.

Thus, with reading becoming so prevalent at home, what happens in school becomes even more significant. The survey shows that reading in school does provide distinctions among young readers. First, children tend to read for fun more at home than in school:

Above copied from Kids and Family Reading Report, 5th Ed.